Modelling population dynamics using age-structured system of partial differential equations

Abstract

In this paper, an age-structured model was used to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was struc- tured into 20 clusters each of 5 year interval, and assigned different birth and death rate parameters. Crank- Nicolson numerical scheme was used to simulate the model and the 2019 initial population of 38,589,011 was found to increase by 50% to 57,956,100 by 2050. The initial economic dependency ratio was computed to be 1:2, but due to changes in technology and improvement of living standards, the new ratio is lowered to 1:1.14. The graphical presentation showed a trend of transition from expansive to constrictive population pyramid